Comparing Spectral Bias and Robustness For Two-Layer Neural Networks: SGD vs Adaptive Random Fourier Features

Abstract: We present experimental results highlighting two key differences resulting from the choice of training algorithm for two-layer neural networks. The spectral bias of neural networks is well known, while the spectral bias dependence on the choice of training algorithm is less studied. Our experiments demonstrate that an adaptive random Fourier features algorithm (ARFF) can yield a spectral bias closer to zero compared to the stochastic gradient descent optimizer (SGD). Additionally, we train two identically structured classifiers, employing SGD and ARFF, to the same accuracy levels and empirically assess their robustness against adversarial noise attacks.